Abstract: This paper presents an analysis of observational data on the p-mode spectrumof the star alpha Cen B and a comparison with theoretical computations of thestochastic excitation and damping of the modes. We find that at frequencies >4500 micro-Hz, the model damping rates appear to be too weak to explain theobserved shape of the power spectral density of alpha Cen B. The conclusionrests on the assumption that most of the disagreement is due to problemsmodelling the damping rates, not the excitation rates, of the modes. Thisassumption is supported by a parallel analysis of BiSON Sun-as-a-star data, forwhich it is possible to use analysis of very long timeseries to place tightconstraints on the assumption. The BiSON analysis shows that there is a similarhigh-frequency disagreement between theory and observation in the Sun.We demonstrate that by using suitable comparisons of theory and observationit is possible to make inference on the dependence of the p-mode linewidths onfrequency, without directly measuring those linewidths, even though the alphaCen B dataset is only a few nights long. Use of independent measures from aprevious study of the alpha Cen B linewidths in two parts of its spectrum alsoallows us to calibrate our linewidth estimates for the star. The resultingcalibrated linewidth curve looks similar to a frequency-scaled version of itssolar cousin, with the scaling factor equal to the ratio of the respectiveacoustic cut-off frequencies of the two stars. The ratio of the frequencies atwhich the onset of high-frequency problems is seen in both stars is also givenapproximately by the same scaling factor.